Q5
(c) What do you mean by reliability and validity of tests ? What is the difference between reliability and validity of a test ? If the reliability of a test is raised from 0·80 to 0·90 by lengthening the test, a validity coefficient of 0·60 for this test would be expected to increase to what value ? 10 marks (d) The rate of increase of a population at time t is r(t) = 0·01 + 0·0001 t². If the population totals 1,000,000 at time t = 0, what is the population at t = 30 ? 10 marks (e) Suggest which of the two measures : Morbidity Incidence rate (MIR) and Morbidity Prevalence rate (MPR) should be used to decide on the amount of medicine to be sent to a Malaria affected area. Cite an example where the other rate can be useful. 10 marks
हिंदी में प्रश्न पढ़ें
(c) परीक्षणों की विश्वसनीयता और वैधता से आप क्या समझते हैं ? एक परीक्षण की विश्वसनीयता और वैधता के बीच क्या अंतर है ? यदि एक परीक्षण की विश्वसनीयता को, परीक्षण को लंबा करके, 0·80 से 0·90 तक बढ़ाया गया, तो इस परीक्षण के लिए वैधता गुणांक 0·60 से बढ़कर कितने मान तक जाना प्रत्याशित होगा ? 10 (d) जनसंख्या वृद्धि दर समय t पर है r(t) = 0·01 + 0·0001 t² यदि समय t = 0 पर कुल जनसंख्या 1,000,000 है, तो समय t = 30 पर जनसंख्या क्या होगी ? 10 (e) दोनों में से कौन-सा उपाय सुझाएं : रुग्णता घटना दर (एम.आई.आर.) और रुग्णता व्यापकता दर (एम.पी.आर.), दवा की मात्रा तय करने के लिए, इसका उपयोग किया जाना चाहिए जो एक मलेरिया प्रभावित क्षेत्र में भेजी जाएगी । एक उदाहरण उद्धृत करें जहाँ अन्य दर उपयोगी हो सकता है । 10
Directive word: Explain
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How this answer will be evaluated
Approach
This question requires explaining three distinct statistical concepts across psychometrics, demography, and epidemiology. Allocate approximately 35% time to part (c) covering reliability, validity definitions, their distinction, and the Spearman-Brown prophecy formula application; 35% to part (d) setting up and solving the differential equation for population growth; and 30% to part (e) comparing MIR and MPR with practical Indian public health examples. Begin with clear conceptual definitions, proceed to mathematical derivations where required, and conclude with contextual interpretations.
Key points expected
- Part (c): Define reliability (consistency/stability of test scores) and validity (extent test measures what it claims to measure); distinguish reliability as necessary but not sufficient for validity; apply Spearman-Brown prophecy formula to calculate new validity coefficient ≈ 0.67
- Part (c): Correctly identify that validity coefficient increases proportionally to square root of reliability ratio: r_new = r_old × √(0.90/0.80) = 0.60 × 1.0607 ≈ 0.636 or 0.64
- Part (d): Set up differential equation dP/dt = P×r(t) = P(0.01 + 0.0001t²); integrate ln(P) = ∫(0.01 + 0.0001t²)dt = 0.01t + 0.0001t³/3 + C
- Part (d): Apply initial condition P(0) = 1,000,000 to find C = ln(10⁶); compute P(30) = 10⁶ × exp[0.01(30) + 0.0001(27000)/3] = 10⁶ × e^1.2 ≈ 3,320,117
- Part (e): Recommend MIR (incidence rate) for medicine allocation as it measures new cases over time, directly indicating current disease burden and transmission dynamics requiring immediate intervention
- Part (e): Cite MPR usefulness for chronic disease planning like diabetes or hypertension prevalence studies in India where total existing cases matter for long-term healthcare infrastructure and resource allocation
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Setup correctness | 20% | 6 | For (c): Correctly defines reliability and validity with psychometric precision; for (d): Properly sets up differential equation with P(0)=10⁶; for (e): Accurately distinguishes MIR (new cases/time) vs MPR (total cases/population) with correct numerator-denominator specification | Basic definitions correct but missing technical nuances; differential equation set up with minor errors in r(t) interpretation; some confusion between incidence and prevalence denominators | Fundamental definitional errors; confuses rate of increase with absolute increase; swaps MIR and MPR definitions or uses wrong denominators |
| Method choice | 20% | 6 | For (c): Applies Spearman-Brown formula correctly; for (d): Uses separation of variables and integration of polynomial rate function; for (e): Applies epidemiological reasoning linking incidence to acute intervention needs and prevalence to chronic disease burden | Correct general approach but misses optimal formula selection; integration performed with minor technique errors; reasonable but incomplete justification for measure selection | Wrong formula applied (e.g., simple proportion for validity); attempts arithmetic instead of calculus for population growth; no logical connection between rate type and public health decision |
| Computation accuracy | 20% | 6 | Part (c): Validity coefficient calculated as 0.636 or 0.64; Part (d): Accurate integration yielding P(30) ≈ 3.32×10⁶ with correct exponent arithmetic (0.3 + 0.9 = 1.2); all intermediate steps shown with precise calculations | Correct final answers with minor arithmetic slips in intermediate steps; exponent calculation slightly off but method recognizable; rounding errors in final presentation | Major calculation errors (e.g., wrong validity coefficient, population magnitude errors); incorrect integration constants; missing or garbled numerical work |
| Interpretation | 20% | 6 | Explains why validity increases sub-proportionally to reliability (square root relationship); interprets 3.32-fold population growth in 30 time units; justifies MIR for malaria medicine with Indian context (e.g., Kerala malaria outbreak response) and MPR for NCDs like Kerala's diabetes prevalence | Basic interpretations provided without depth; mentions population 'increases' without magnitude context; generic public health examples without Indian specificity | No interpretation of results; fails to explain why specific rate was chosen; missing real-world application entirely |
| Final answer & units | 20% | 6 | Clear final answers: (c) validity ≈ 0.64 or 0.636; (d) P(30) ≈ 3,320,000 or 3.32×10⁶ with proper units; (e) explicit MIR recommendation with coherent justification; all answers boxed/highlighted and dimensionally consistent | Correct answers present but poorly formatted; units missing or inconsistent; final recommendation stated without supporting reasoning | Missing final answers; wrong units (e.g., population in thousands instead of actual); contradictory recommendations; incomplete responses for one or more parts |
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